Essential University Physics, 3e (Wolfson) 3e (Wolfson) Chapter 6 Work, Work, Energy, and Power
6 . 1 Conc e p t ua lQue s t i o ns 1) If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other. A) True B) False Answer: A ar: 1
!) If two nonzero vectors point in the same direction, their dot product must be zero. A) True B) False Answer: B ar: 1
") The value of the dot product of two vectors depends on the particular coordinate s#stem bein$ used. A) True B) False Answer: B ar: 1
%) Two Two men, &oel and &err#, push a$ainst a wall. &err# stops after 1' min, while &oel is able to push for (.' min lon$er. ompare ompare the wor* the# do. A) Both men do positive wor*, but &oel does +( more wor* than &err#. &err#. B) Both men do positive wor*, but bu t &oel does (' more wor* than &err#. &err#. ) Both men do positive wor*, but bu t &err# does (' more wor* than &oel. -) Both men do positive wor*, but &oel does !( more wor* than &err#. &err#. ) /either of them does an# wor*. Answer: ar: 1
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() A stoc* person at the local $rocer# store has a 0ob consistin$ of the followin$ five se$ments: 1) pic*in$ up bo2es of tomatoes from the stoc*room floor !) acceleratin$ to a comfortable speed ") carr#in$ the bo2es to the tomato displa# at constant speed %) deceleratin$ to a stop () lowerin$ the bo2es slowl# to the floor. -urin$ which of the five se$ments of the 0ob does the stoc* person do positive wor* on the bo2es3 A) 1) and () B) 1) onl# ) 1), !), %), and () -) 1) and !) ) !) and ") Answer: ar: 1
4) A ".''5*$ ball swin$s rapidl# in a complete vertical circle of radius !.'' m b# a li$ht strin$ that is fi2ed at one end. The ball moves so fast that the strin$ is alwa#s taut and perpendicular p erpendicular to the velocit# of the ball. As the ball swin$s from its lowest point to its hi$hest point A) the wor* done on it b# $ravit# and the wor* done on it b# the tension in the strin$ are both e6ual to 5117 &. B) the wor* done on it b# $ravit# is 5117 & and the wor* done on it b# the tension in the strin$ is 8117 &. ) the wor* done on it b# $ravit# is 8117 & and the wor* done on it b# the tension in the strin$ is 5117 &. -) the wor* done on it b# $ravit# is 5117 & and the wor* done on it b# the tension in the strin$ is zero. ) the wor* done on it b# $ravit# and the wor* done on it b# the tension in the strin$ are both e6ual to zero. Answer: ar: 1
+) onsider a plot of the displacement x) as a function of the applied force F F ) for an ideal elastic sprin$. The slope of the curve would be A) the sprin$ constant. B) the reciprocal of the sprin$ constant. ) the acceleration due to $ravit#. -) the reciprocal of the acceleration of $ravit# $ ravit#.. ) the mass of the ob0ect attached to the sprin$. Answer: B ar: 1
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7) 9hich of the $raphs in the fi$ure illustrates oo*e;s
A) =raph a B) =raph b ) =raph c -) $raph d Answer: B ar: 1
>) 9hich of the $raphs in the fi$ure represents a sprin$ that $ets less stiff the more it is stretched3
A) =raph a B) =raph b ) =raph c -) =raph d Answer: ar: 1
1') A %.'5*$ ob0ect is movin$ with speed !.' m?s. A 1.'5*$ ob0ect is movin$ with speed %.' m?s. 3 Copyright © 2016 Pearson Education, Inc.
Both ob0ects encounter the same constant bra*in$ force, and are brou$ht to rest. 9hich ob0ect travels the $reater distance before stoppin$3 A) the %.'5*$ ob0ect B) the 1.'5*$ ob0ect ) Both ob0ects travel the same distance. -) It is impossible to *now without *nowin$ how lon$ each force acts. Answer: ar: 1
11) If a force alwa#s acts perpendicular to an ob0ect;s direction o f motion, that force cannot chan$e the ob0ect;s *inetic ener$#. A) True B) False Answer: A ar: 1
1!) Three cars car F , car G, and car H ) are movin$ with the same velocit# when the driver suddenl# slams on the bra*es, loc*in$ the wheels. The most massive car is car F , the least massive is car H , and all three cars have identical tires. a) 9hich car travels the lon$est distance to s*id to a stop3 A) ar F B) ar G ) ar H -) The# all travel the same distance in stoppin$. b)
For which car does friction do the lar$est amount of wor* in stoppin$ the car3 A) ar F B) ar G ) ar H -) The amount of wor* done b# friction is the same for all cars. Answer: a) - b) A ar: 1
1") Two ob0ects, one of mass m and the other of mass !m, are dropped from the top of a buildin$. 9hen the# hit the $round A) both of them will have the same *inetic ener$#. B) the heavier one will have twice the *inetic ener$# of the li$hter one. ) the heavier one will have four times the *inetic ener$# of the li$hter one. -) the heavier one will have times the *inetic ener$# of the li$hter one. Answer: B ar: 1
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6 . 2 Pr o bl e ms 1) -etermine the scalar product of
@ 4.' 8 %.' 5 !.' and
@ (.' 5 4.' 5 ".' .
A) "' 8 !% 8 4 B) "' 5 !% 8 4 ) 1! -) 4' ) undefined Answer: ar: (
!) -etermine the an$le between the directions of vector
@ ".'' 8 1.'' and vector
@ 5".''
8 ".'' . A) !4.4 B) "'.' ) 77.1 -) 11+ ) %(.! Answer: ar: (
") The scalar product of vector vectors could be vector
@ ".'' 8 !.'' and vector
is 1'.'. 9hich of the followin$
3
A) !.'' 8 %.'' B) %.'' 8 4.'' ) (.'' 8 %.'' -) 1!.' ) !.'' 8 !.'' Answer: ar: (
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%) The an$le between vector vectors
and
@ !.'' 8 ".'' and vector
is ".''. If the x component of vector
is
The scalar product of
is positive, what is vector
.
A) B) ) -) ) Answer: B ar: (
() 9hat is the an$le between the vector
@ 8" 5 ! 5 " and the 8 y5a2is3
A) 11( B) 4( ) !( -) 1(( ) >' Answer: A ar: 14
4) If
@ " 5 8 % and
@ x 8 5 ( , find x so
will be perpendicular to
.
Answer: + ar: 1
+) Two bo#s searchin$ for buried treasure are standin$ underneath the same tree. ne bo# wal*s east and then north. The other bo# wal*s west and then north. Find the scalar product of their net displacements from the tree. Answer: 5>' ar: ('8
7) A rectan$ular bo2 is positioned with its vertices at the followin$ points: A @ ',',') C @ !,%,') E @ ',',") G @ !,%,") B @ !,',') D @ ',%,') F @ !,',") H @ ',%,") If the coordinates all have three si$nificant fi$ures, the an$le between the line se$ments AG and AH is closest to: A) !1.7. B) !!.(. ) !4.4. -) "4.>. ) %(.'. Answer: A ar: 1
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>) For the vectors shown in the fi$ure, assume numbers are accurate to two si$nificant fi$ures. The scalar product
C
is closest to
A) zero. B) 14. ) %(. -) 514. ) 5%(. Answer: ar: 1
1') Three forces, F 1 @ !'.' /, F ! @ %'.' /, and F " @ 1'.' / act on an ob0ect with a mass of !.'' *$ which can move alon$ a frictionless inclined plane as shown in the fi$ure. The 6uestions refer to the instant when the ob0ect has moved throu$h a distance of '.4'' m alon$ the surface of the inclined plane in the upward direction. alculate the amount of wor* done b# a) F 1 b) F ! c) F ".
Answer: a) 1!.' &
b) !'.7 &
c) '.'' &
ar: 1
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11) Dou carr# a +.' *$ ba$ of $roceries above the level floor at a constant velocit# of +( cm?s across a room that is room. ow much wor* do #ou do on the ba$ in the process3 A) '.' & B) 7! & ) 1(7 & -) 1"% & Answer: A ar: ('8
1!) A student slides her 7'.'5*$ des* across the level floor of her dormitor# room a distance %.'' m at constant speed. If the coefficient of *inetic friction between the des* and the floor is '.%'', how much wor* did she do3 A) 1!7 & B) ".1% *& ) !4.+ & -) 1.!4 *& ) !%.' & Answer: ar: (
1") Find the net wor* done b# friction on the bod# of a sna*e slitherin$ in a complete circle of radius. The coefficient of friction between the $round and the sna*e is '.!(, and the sna*e;s wei$ht is A) 5""' & B) ' & ) 5""'' & -) 54+' & Answer: A ar: ('8
1%) A crane lifts a %!( *$ steel beam verticall# a distance of
ow much wor* does the
crane do on the beam if the beam accelerates upward at 1.7 m?s!3 /e$lect frictional forces. A) (.7 × 1'( & B) ".% × 1'( & ) %.' × 1'( & -) %.> × 1'( & Answer: A ar: ('8
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1() An airplane flies 1!' *m at a constant altitude in a direction "'.' north of east. A wind is blowin$ that results in a net horizontal force on the plane due to the air of !.%' */ in a direction 1'.' south of west. ow much wor* is done on the plane b# the air3 A) 5!.+1 C 1'7 & B) 5'.>7( C 1'7 & ) 5!!1 C 1'7 & -) !!1 C 1'7 & ) '.7!1 C 1'7 & Answer: A ar: 1
14) A traveler pulls on a suitcase strap at an an$le "4 above the horizontal. If of wor* are done b# the strap while movin$ the suitcase a horizontal distance of 1( m, what is the tension in the strap3 A) +( / B) 41 / ) 7( / -) >! / Answer: A ar: ('8
1+) An ob0ect is acted upon b# a force that represented b# the force vs. position $raph in the fi$ure. 9hat is the wor* done as the ob0ect moves a) from % m to 4 m3 b) from 4 m to 1! m3
Answer: a) !' &
b) "' &
ar: 1
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17) In the fi$ure, a constant e2ternal force P @ 14' / is applied to a !'.'5*$ bo2, which is on a rou$h horizontal surface. 9hile the force pushes the bo2 a distance of 7.'' m, the speed chan$es from '.('' m?s to !.4' m?s. The wor* done b# friction durin$ this process is closest to
A) 51'%' &. B) 8111' &. ) 811+' &. -) 81'%' &. ) 511+' &. Answer: A ar: 1
1>) In the fi$ure, a +''5*$ crate is on a rou$h surface inclined at "'. A constant e2ternal force P @ (4'' / is applied horizontall# to the crate. As the force pushes the crate a distance of ".'' m up the incline, the speed chan$es from 1.%' m?s to !.(' m?s. ow much wor* does $ravit# do on the crate durin$ this process3
A) 51',"'' & B) 5"%'' & ) 81',"'' & -) 8"%'' & ) zero Answer: A ar: 1
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!') A $raph of the force on an ob0ect as a function of its position is shown in the fi$ure. -etermine the amount of wor* done b# this force on an ob0ect that moves from x @ 1.' m to x @ 4.' m. Assume an accurac# of ! si$nificant fi$ures for the numbers on the $raph.)
A) !4 & B) !> & ) !! & -) "( & ) !+ & Answer: A ar: (
!1) A $raph of the force on an ob0ect as a function of its position is shown in the fi$ure. -etermine the amount of wor* done b# this force on the ob0ect durin$ a displacement from x @ 5!.'' m to x @ !.'' m. Assume an accurac# of " si$nificant fi$ures for the numbers on the $raph.)
A) 51!.' & B) 5".'' & ) 51.'' & -) 1!.' & ) ".'' & Answer: ar: 1
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!!) A force
@ 1! / 5 1' / acts on an ob0ect. ow much wor* does this force do as the
ob0ect moves from the ori$in to the point A) %4 & B) !44 & ) "+ & -) 4! & Answer: A ar: 7
!") A sprin$ stretches b# that would stretch the sprin$ b# A) 1>> / B) >1.' / ) 1%( / -) !+> / Answer: A
when a
ob0ect is attached. 9hat is the wei$ht of a fish
ar: ('8
!%) An ob0ect attached to an ideal massless sprin$ is pulled across a frictionless surface. If the sprin$ constant is %( /?m and the sprin$ is stretched b# '.77 m when the ob0ect is acceleratin$ at what is the mass of the ob0ect3 A) !' *$ B) 1+ *$ ) !! *$ -) !4 *$ Answer: A ar: 17
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!() In the fi$ure, two identical ideal massless sprin$s have unstretched len$ths of '.!( m and sprin$ constants of +'' /?m. The sprin$s are attached to a small cube and stretched to a len$th L of '."' m as in Fi$ure A. An e2ternal force P pulls the cube a distance D @ '.'!' m to the ri$ht and holds it there. Eee Fi$ure B.) The e2ternal force P , that holds the cube in place in Fi$ure B, is closest to
A) !7 /. B) !( /. ) !1 /. -) 17 /. ) 1% /. Answer: A ar: 1
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!4) Bloc* A '.%' *$) and bloc* B '."' *$) are on a frictionless table see fi$ure). Eprin$ 1 connects bloc* A to a frictionless pe$ at 0 and sprin$ ! connects bloc* A and bloc* B. 9hen the bloc*s are in uniform circular motion about 0, the sprin$s have len$ths of '.4' m and '.%' m, as shown. The sprin$s are ideal and massless, and the linear speed of bloc* B is !.' m?s. If the distance that sprin$ ! stretches is '.'4' m, the sprin$ constant of sprin$ ! is closest to
A) 17 /?m. B) !' /?m. ) !! /?m. -) !% /?m. ) !4 /?m. Answer: B ar: 1
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!+) Bloc* A '.%' *$) and bloc* B '."' *$) are on a frictionless table see fi$ure). Eprin$ 1 connects bloc* A to a frictionless pe$ at 0 and sprin$ ! connects bloc* A and bloc* B. 9hen the bloc*s are in uniform circular motion about 0, the sprin$s have len$ths of '.4' m and '.%' m, as shown. The sprin$s are ideal and massless, and the linear speed of bloc* B is !.' m?s. If the sprin$ constant of sprin$ 1 is e6ual to "' /?m, the unstretched len$th of sprin$ 1 is closest to
A) '.(1 m. B) '.(! m. ) '.(" m. -) '.(% m. ) '.(( m. Answer: ar: 1
!7) A force on a particle depends on position such that F x) @ ".'' /? ) 8 4.'' /?m) x for a particle constrained to move alon$ the 25a2is. 9hat wor* is done b# this force on a particle that moves from x @ '.'' m to x @ !.'' m3 A) 1'.' & B) !'.' & ) 5%7.' & -) !%.' & ) %7.' & Answer: B ar: (
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!>) A person pushes horizontall# on a heav# bo2 and slides it across the level floor at constant velocit#. The person pushes with a 4'.' / force for the first at which time he be$ins to tire. The force he e2erts then starts to decrease linearl# from 4'.' / to '.'' / across the remainin$ ow much total wor* did the person do on the bo23 A) 41> & B) 7!4 & ) %>( & -) >!( & Answer: A ar: ('8
"') It re6uires %> & of wor* to stretch an ideal ver# li$ht sprin$ from a len$th of 1.% m to a len$th of !.> m. 9hat is the value of the sprin$ constant of this sprin$3 A) 1( /?m B) %% /?m ) !> /?m -) !! /?m Answer: A ar: ('8
"1) A force F = bx" acts in the x direction, where the value of b is ".+ /?m". ow much wor* is done b# this force in movin$ an ob0ect from to A) %! & B) 1" & ) (' & -) (+ & Answer: A ar: 1"
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"!) In the fi$ure, two identical sprin$s have unstretched len$ths of '.!( m and sprin$ constants of "'' /?m. The sprin$s are attached to a small cube and stretched to a len$th L of '."4 m as in Fi$ure A. An e2ternal force P pulls the cube a distance D @ '.'!' m to the ri$ht and holds it there. Eee Fi$ure B.) The wor* done b# the e2ternal force P in pullin$ the cube '.'!' m is closest to
A) '.1! &. B) '.'4' &. ) 4.' &. -) 1! &. ) '.7' &. Answer: A ar: 1
"") A 1'''.' *$ car is movin$ at the car, how fast is the truc* movin$3 A) %( *m?h B) 4" *m?h ) (% *m?h -) "4 *m?h Answer: A
If a
truc* has 17 times the *inetic ener$# of
ar: ('8
"%) ow much ener$# is needed to chan$e the speed of a 14'' *$ sport utilit# vehicle from 1(.' m?s to %'.' m?s3 A) 1.1' & B) 1'.' *& ) !'.' *& -) %'.' *& ) '.>4' & Answer: A ar: 1
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"() The coefficient of the restitution of an ob0ect is defined as the ratio of its out$oin$ to incomin$ speed when the ob0ect collides with a ri$id surface. For an ob0ect with a coefficient of '.+7, what fraction of the ob0ect;s *inetic ener$# is lost durin$ a sin$le collision3 A) "> B) 14 ) %+ -) 41 Answer: A ar: "1
"4) A wor*er lifts a !'.'5*$ buc*et of concrete from the $round up to the top of a !'.'5m tall buildin$. The buc*et is initiall# at rest, but is travelin$ at %.' m?s when it reaches the top of the buildin$. 9hat is the minimum amount of wor* that the wor*er did in liftin$ the buc*et3 A) ".>! *& B) %'' & ) (4' & -) %.'7 *& ) 14' & Answer: ar: (
"+) A ball is thrown upward at an an$le with a speed and direction such that it reaches a ma2imum hei$ht of 14.' m above the point it was released, with no appreciable air resistance. At its ma2imum hei$ht it has a speed of 17.' m?s. 9ith what speed was the ball released3 A) !(." m?s B) !!.! m?s ) "".' m?s -) !>.! m?s ) "4.> m?s Answer: A ar: (
"7) A 1''' *$ car e2periences a net force of >('' / while deceleratin$ from "'.' m?s to !".% m?s. ow far does it travel while slowin$ down3 A) 17.( m B) 1+.% m ) !'.! m -) !1.> m Answer: A ar: 1
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">) A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. 9hen the pull acts over a distance x, the sled ac6uires a speed v and a *inetic ener$# K . If the same pull instead acts over twice this distance: A) The sledGs speed will be !v and its *inetic ener$# will be ! K . B) The sledGs speed will be !v and its *inetic ener$# will be K . ) The sledGs speed will be v
and its *inetic ener$# will be ! K .
-) The sled;s speed will be v and its *inetic ener$# will be K . ) The sled;s speed will be %v and its *inetic ener$# will be ! K. Answer: ar: 1
%') In the fi$ure, a >''5*$ crate is on a rou$h surface inclined at "'. A constant e2ternal force is applied horizontall# to the crate. 9hile this force pushes the crate a distance of ".' m up the incline, its velocit# chan$es from 1.! m?s to !." m?s. ow much wor* does friction do durin$ this process3
A) 5"+'' & B) 5+!'' & ) 8"+'' & -) 8+!'' & ) zero Answer: A ar: ('8
%1) A (.''5*$ bo2 slides %.'' m across the floor before comin$ to rest. 9hat is the coefficient of *inetic friction between the floor and the bo2 if the bo2 had an initial speed of ".'' m?s3 A) 1.1" B) '.(7+ ) '.11( -) '.!!> ) '.!4+ Answer: ar: (
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%!) Dou slam on the bra*es of #our car in a panic, and s*id a certain distance on a strai$ht, level road. If #ou had been travelin$ twice as fast, what distance would the car have s*idded, under identical conditions3 A) It would have s*idded % times farther. B) It would have s*idded ! times farther. ) It would have s*idded times farther. -) It would have s*idded 1? times farther. ) It would have s*idded 1?! as far. Answer: A ar: 1
%") In the fi$ure, two bo2es, each of mass !% *$, are at rest and connected as shown. The coefficient of *inetic friction between the inclined surface and the bo2 is '."1. Find the speed of the bo2es 0ust after the# have moved 1.4 m.
Answer: 1.> m?s ar: 1
%%) A %.''5*$ mass is attached to a ver# li$ht ideal sprin$ han$in$ verticall# and han$s at rest in the e6uilibrium position. The sprin$ constant of the sprin$ is 1.'' /?cm. The mass is pulled downward !.'' cm and released. 9hat is the speed of the mass when it is 1.'' cm above the point from which it was released3 A) '.'%%" m?s B) '.'+%% m?s ) '.'!'1 m?s -) '.'744 m?s ) The mass will not reach the hei$ht specified. Answer: ar: (
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%() An unusual sprin$ has a restorin$ force of ma$nitude F @ !.'' /?m) x 8 1.'' /?m!) x!, where x is the stretch of the sprin$ from its e6uilibrium len$th. A ".''5*$ ob0ect is attached to this sprin$ and released from rest after stretchin$ the sprin$ 1.(' m. If the ob0ect slides over a frictionless horizontal surface, how fast is it movin$ when the sprin$ returns to its e6uilibrium len$th3 A) !.'4 m?s B) %."" m?s ) ".!+ m?s -) (.%7 m?s ) 1.(' m?s Answer: ar: (
%4) The force on a ".''5*$ ob0ect as a function of position is shown in the fi$ure. If an ob0ect is movin$ at !.(' m?s when it is located at x @ !.'' m, what will its speed be when it reaches x @ 7.'' m3 Assume that the numbers on the $raph are accurate to " si$nificant fi$ures.)
A) ".!( m?s B) ".+' m?s ) %.1' m?s -) !.>' m?s ) %.(' m?s Answer: A ar: 1
%+) A +.'5*$ roc* is sub0ect to a variable force $iven b# the e6uation F x) @ 4.' / 5 !.' /?m) x 8 4.' /?m!) x! If the roc* initiall# is at rest at the ori$in, find its speed when it has moved >.' m. Answer: !' m?s ar: 1
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%7) A 1(''5*$ car accelerates from ' to !( m?s in +.' s with ne$li$ible friction and air resistance. 9hat is the avera$e power delivered b# the en$ine3 1 hp @ +%4 9) A) (' hp B) 4' hp ) +' hp -) 7' hp ) >' hp Answer: ar: 1
%>) A child pulls on a wa$on with a horizontal force of If the wa$on moves horizontall# a total of in what is the avera$e power $enerated b# the child3 A) 17 9 B) !! 9 ) !% 9 -) !+ 9 Answer: A ar: !>
(') A car needs to $enerate in order to maintain a constant velocit# of on a flat road. 9hat is the ma$nitude of the total resistive force actin$ on the car due to friction, air resistance, etc.)3 1 hp @ +%4 9) A) !.'( × 1'" / B) !.+( / ) 1.'" × 1'" / -) !.7+ × 1'" / Answer: A ar: ('8
(1) ow lon$ will it ta*e a +.'7 hp motor to lift a !(' *$ beam directl# upward at constant velocit# from the $round to a hei$ht of %(.' m3 Assume frictional forces are ne$li$ible. 1 hp @ +%4 9) A) !'.> s B) 1.(4 × 1'% s ) !.17 × 1'% s -) ">.+ s Answer: A ar: ('8
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(!) alculate the minimum avera$e power output necessar# for a person to run up a 1!.' m lon$ hillside, which is inclined at !(.' above the horizontal, in ".'' s. Dou can ne$lect the person;s *inetic ener$#. 2press #our answer in horsepower. 1 hp @ +%4 9) A) 1.!% hp B) !.>" hp ) 1.74 hp -) '.+%' hp Answer: A ar: ('8
(") If electricit# costs 4.''H?*9h *ilowatt5hour), how much would it cost #ou to run a 1!' 9 stereo s#stem %.' hours per da# for %.' wee*s3 A) '.71 B) '.1! ) 1."7 -) !.!+ Answer: A ar: ('8
(%) The wor* performed as a function of time for a process is $iven b# 9hat is the instantaneous power output at A) >> 9 B) 4> 9 ) 1"> 9 -) !'7 9 Answer: A ar: !4
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where
